A $\sqrt{n}$ estimate in the hyperplane problem with arbitrary measures has recently been proved in \cite{K3}. In this note we present analogs of this result for sections of lower dimensions and in the complex case. We deduce these inequalities from stability in comparison problems for different generalizations of intersection bodies.
Measures of sections of convex bodies
A $sqrt{n}$ estimate for measures of hyperplane sections of convex bodies
On strict inclusions in hierarchies of convex bodies
![QR code for arXiv:1309.6485 [math.MG]](http://oss.arxitics.com/images/favicon.svg)